Randomizing the starting frame of an image sequence on a per object basis
The only workaround I have in mind is to use drivers.
Try plugging the random output to a Math node where you add 0 to it (just to have the value in some place you can address with a driver) and set a driver to the offset value, pointing the driver to the value in the Math node where you plugged the random.
I didn't try it yet, so I'm not 100% sure it will work.
If it doesn't let me know. Another alternative is to use Python.